Equimorphy: the case of chains
- 98 Downloads
Two structures are said to be equimorphic if each embeds in the other. Such structures cannot be expected to be isomorphic, and in this paper we investigate the special case of linear orders, here also called chains. In particular we provide structure results for chains having less than continuum many isomorphism classes of equimorphic chains. We deduce as a corollary that any chain has either a single isomorphism class of equimorphic chains or infinitely many.
KeywordsEquimorphy Embedding Isomorphic
Mathematics Subject Classification06A05 03C64 03E04
Unable to display preview. Download preview PDF.
The first author warmly thanks the Logic group and their staff at the Institut Camille Jordan of Université Lyon I for their wonderful hospitality during the final preparation of this work. The second author thanks the Department of Mathematics and Statistics of the University of Calgary where this research started in the summer of 2012 and for the stimulating atmosphere and support. All three authors thank the referee for valuable comments.
- 4.Diestel, R.: Graph Theory. Graduate Texts in Mathematics, vol. 173, 4th edn. Springer, Heidelberg (2010)Google Scholar
- 11.Jullien, P.: Contribution à l’étude des types d’ordres dispersés, Thèse Doctorat d’État, Université de Marseille, 27 juin 1968 (1968)Google Scholar
- 16.Rosenstein, J.G.: Linear Orderings, Pure and Applied Mathematics, vol. 98. Academic Press, Harcourt Brace Jovanovich, New York, London (1982)Google Scholar
- 18.Thomassé, S.: Conjectures on Countable Relations. Pers. Commun. (2012)Google Scholar